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Proof step 6 from proof cast-b2i-01 (previous step)

i = i0 + 1, 8 ≤ i, 0 < i ⊦ cast(i, b2i(by)) = b2i(by), 0 = i, ¬ 2 ^ i0 ≤ b2i(by) ∧ ¬ 2 ^ i0 + b2i(by) < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
7 ≤ i0, 0 < i0, 0 ≤ i0 ⊦ cast(i0 + 1, b2i(by)) = b2i(by), ~1 = i0, ¬ 2 ^ i0 ≤ b2i(by) ∧ ¬ 2 ^ i0 + b2i(by) < 0

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;